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1 SUPPLEMENTARY INFORMATION doi:1.138/nature Theoretical framework The theoretical results presented in the main text and in this Supplementary Information are obtained from a model that describes the behaviour of a single impurity embedded in a Fermi sea with tuneable s-wave interaction near a Feshbach resonance with arbitrary effective range. Two different wavefunctions are needed, depending on whether one is interested in the polaron 1, 2 or molecule 3 5 properties. The quasiparticle parameters for the polaron (energy E + and E, residue Z, effective mass) and the molecule properties can be found either variationally, or diagrammatically using the ladder approximation. Both approaches yield identical results, which closely match independent Monte-Carlo calculations 6. The properties of the repulsive polaron, which is intrinsically unstable due to the presence of the molecule-hole continuum (MHC) and of the attractive polaron, are obtained from the self energy. In particular, the interaction induced energy shift and the decay rate are given by the real part and twice the imaginary part of the self energy, respectively 7. Previous treatments 1 7 were based on a universal scattering amplitude, describing broad Feshbach resonances. To include effects of the finite effective range we employ a many-body T-matrix given by 8, 9 [ ] m 1 r T (K,ω)= 2π h 2 ã(k,ω) Π(K,ω). (1) Here hk = p K + p Li is the total momentum with p Li and p K the momenta of 6 Li and 4 K,m r = m Li m K /(m Li + m K ) the reduced mass, Π(K,ω) the) 6 Li - 4 K pair propagator in the presence of B the Fermi sea, and ã(k,ω) a bg (1 B B E CM /δµ an energy-dependent length parameter, with a bg, B, B, and δµ being the background scattering length, the width, the center, and the relative magnetic moment of the Feshbach resonance. E CM (K,ω) = hω h 2 K 2 /(2M)+ε F, with M = m Li + m K, is the energy in the center of mass reference frame of the colliding pair. In vacuum and close to resonance, the scattering amplitude of our model has the usual low energy expansion fk 1 = a 1 + ik r e k 2 /2 +..., (2) with the relative momentum hk =(m Li p K m K p Li )/M. The effective range is approximated by r e 2R (1 a bg /a) 2, where we introduce the range parameter R = h 2 /(2m r a bg Bδµ), see Ref. 1. Within the one particle-hole approximation, the energies E ± of the repulsive and attractive polarons at zero temperature are given by the two solutions of the implicit equation E ± = p2 K 2m K + Re[Σ(p K,E ± )], (3) where the self-energy describing the interactions of the impurity with the bath reads 2 Σ(p K,ω)= ( ) T p K + p Li,ω + p2 Li ε F. (4) p Li <k F 2m Li 1

2 RESEARCH SUPPLEMENTARY INFORMATION ( ) The residue of polarons with vanishing momentum, which we plot in Fig. 4c of the main paper, are given by [ [ ] ] 1 Σ(pK =,ω) Z ± = 1 Re. (5) ω A more detailed theoretical analysis of this model is given in Ref Polaron peak in the spectral response The spectra in Fig. 2a of the main text show a narrow, coherent peak on top of a spectrally broad, incoherent background. Here, we investigate these two spectral parts in more detail. Note that the background is actually better visible in Fig. 2b, but these spectra do not allow for a quantitative comparison of the two parts because of the strong saturation of the narrow polaron peaks. The narrow peak stems from the attractive or repulsive polarons, which correspond to well defined energy levels, provided that the lifetime of the quasiparticle exceeds the pulse duration. As a consequence, the lineshape is expected to be Fourier limited except for the rapidly decaying repulsive polarons very close to resonance. In contrast, the background is spectrally wide, on the order of ε F. The main contribution to the background stems from the MHC. Another contribution may arise from the excitation of additional particle-hole pairs in the Fermi sea when transferring to a quasiparticle with a momentum that is different from the momentum of the impurity in the initial state. We distinguish between the narrow peak and the wide background by means of a double Gauss fit. Vertical cuts through Fig. 2a are presented in Fig. S1a together with the fit curves. The width σ p of the Gauss function fitting the narrow peak is fixed to the one associated with the Gaussian fit of the Blackman pulse line shape used in the experiment, σ p =.7kHz=.19ε F /h. We constrain the width σ b of the Gauss function reproducing the background to 3.19ε F /h < σ b <.5ε F /h. The lower bound avoids the misinterpretation of the narrow peak as background and the upper bound, corresponding to the maximal width of the continuum as obtained from the spectra in Fig. 2b, avoids unphysically large values of σ b when the background signal is weak. We find that the narrow peak dominates for weak positive and negative interaction strength while the wide background dominates in the strongly interacting regime. This trend is shown in Fig. S1b and Fig. S1c, where we present the maximum signal of the narrow peak and the area of the background, respectively. Note, that the signal in Fig. S1b is proportional to the area of the narrow E ± 2

3 SUPPLEMENTARY INFORMATION RESEARCH a 1/(κ F a) Signal /ε F b 1 height of narrow peak c norm. area of background d peak /ε F /(κ F a) Supplementary Figure 1: Double Gauss analysis of the low-power spectra. The data are the same as presented in Fig. 2a plus additional data in an extended range of 1/(κ F a). (a) The Gauss function fitting the wide background is shaded grey. The Fourier-limited Gauss function, fitting the narrow peak, is coloured red (green) along the repulsive (attractive) polaron branch. We identify the narrow peak with one of the polaron branches only if its maximum signal exceeds a threshold value of.85, corresponding to two times the standard deviation of the noise in our data. Any smaller peak may be caused by fitting to a noise component. The lower panels show (b) the maximum signal of the narrow peak with the dashed line indicating the threshold, (c) the area under the wide Gauss function normalized to its maximum value, and (d) the detuning at the center of the narrow peak, provided that the peak signal exceeds the threshold, compared to the theoretical calculation of E + and E (red and green line). The error bars indicate the fit uncertainties

4 RESEARCH SUPPLEMENTARY INFORMATION peak since σ p is kept constant. Figure S1d shows the detuning at the center of the narrow peak, which corresponds to the energy of the quasiparticles. The measured energies agree remarkably well with the calculation. The slight mismatch between theory and experiment may be attributed to systematic errors in the determination of ε F and B. The area of the wide background exhibits a maximum close to 1/(κ F a)=, but it shows an asymmetry as it falls off significantly slower on the attractive (a < ) side, see Fig. S1c. We attribute this asymmetry to the narrow character of the Feshbach resonance. The interaction becomes resonant when the real part of the inverse scattering amplitude, given in Eq. 2, is zero. This leads to the resonance condition a 1 res = r e k 2 /2, where a res is the value of the scattering length at which the interaction becomes resonant. In the limit of a broad resonance with r e =, this condition is fulfilled for any k at the center of the resonance, where the scattering length diverges. However, at a narrow resonance with r e < the condition requires a negative a res for k >. The mean square momentum in the Fermi sea is 3/5 κf 2, leading to a mean square relative momentum of 3/5 (4/46 κ F ) 2. Using this value for k 2, and inserting r e 2R in the above resonance condition, we obtain 1/(κ F a)=.43. This represents an effective shift of the Feshbach resonance center, as we average over all momenta of the Fermi sea 12. The magnitude of this shift agrees well with the observed asymmetry. Moreover, we find that many features at our narrow resonance appear to be shifted, e.g. the polaron-to-molecule crossing. However, the narrowness has many more implications and cannot simply be reduced to this shift. We will come back to this point in the context of the lifetime of the repulsive polaron, see Sec. 4. The repulsive polaron peak is clearly visible up to 1/(κ F a).3 while the attractive polaron peak vanishes already at 1/(κ F a).9, see Fig. S1b. The fading out of the quasiparticle peak towards the strongly interacting regime approximately coincides with the position where the quasiparticle branches merge into the MHC. This shows that the polaron state is hardly observable as soon as it becomes degenerate with molecule-hole excitations. The MHC is not strictly limited to the range from E m to E m ε F, as discussed in more detail in Sec. 3. It extends below E m ε F because of finite temperature effects. It also extends slightly above E m because of additional excitations in the spectral function of the molecules 13. As a consequence, for finite temperature, the attractive polaron can become degenerate with molecule-hole excitations for values of the interaction parameter above the calculated polaron-to-molecule crossing. This explains that the observed sharp peak is observed to disappear already at 1/(κ F a).9, which lies somewhat above the zero-temperature polaron-to-molecule crossing predicted at.6. It is interesting to consider the data analysis presented in Fig. S1b and c in relation to the common method of extracting the quasiparticle residue Z from the spectral weight of the narrow peak 14. Close to resonance, we are in the linear response regime and our data can be interpreted in terms of this method. Our data suggests that this method leads to a significant underestimation of Z. For example at 1/(κ F a).9, where the narrow peak of the attractive polaron vanishes, our theory still predicts Z.7. This underestimation is consistent with the one reported in Ref. 15, see also related discussion in Ref. 4. A plausible explanation may be that such a method does not probe the polaron states alone, but also the molecule-hole excitations, which are degenerate with the polaron state. Our alternative method of measuring the residue via the Rabi frequency, as presented in the main paper, offers the advantage of being much less affected by the molecule- 4

5 SUPPLEMENTARY INFORMATION RESEARCH 1 1/(κ F a) = /(κ F a) = 1.6 /ε F Signal /(κ F a) = 1.3 /ε F /ε F Supplementary Figure 2: Molecule association spectra for different values of the interaction parameter. The signal is the fraction of transferred atoms as a function of the rf detuning. The data correspond to vertical cuts through Fig. 2b. The dashed line is the line shape model for zero temperature and the solid line for finite temperature. The upper threshold of the theoretical spectra corresponds to E m. hole contribution. In fact, only the coherent part of the quasiparticle is expected to produce Rabi oscillations, see Sec Molecule-hole continuum The spectra presented in Fig. 2b of the main text reveal the MHC. This continuum arises from processes where the rf field associates a 4 K impurity and a 6 Li atom out of the Fermi sea to a molecule. Here we present a simple model for the spectral line shape, which allows us to interpret the data up to 1/(κ F a) 1, see Fig S2. For modeling the line shape, we consider two-body processes in which the rf field associates one 4 K and one 6 Li atom to a molecule. Higher-order processes, involving more than two particles, are neglected in this model but are briefly discussed at the end of this section. Let us first consider the association of 6 Li and 4 K with momenta p Li = p K =. This results in a molecule at rest plus a Fermi sea with a hole in the center. The energy of this state is determined by the binding energy of the molecule and by the interaction of the molecule with the Fermi sea. It is given by E m and sets the onset of the MHC from the right (the top) in Fig. S2 (Fig. 2b). In general, 6 Li and 4 K have finite initial relative momentum hk, leading to an initial relative kinetic energy in the center 5

6 RESEARCH SUPPLEMENTARY INFORMATION of mass frame E r = h 2 k 2 /2m r. The energy conservation of the association process is expressed in the Dirac δ function in Eq. 6. As a consequence, the molecule spectrum extends downwards to energies below E m. We now consider an ensemble of 4 K and 6 Li atoms. Our experimental conditions are well approximated by a thermal cloud of 4 K in a homogeneous Fermi sea of 6 Li (see Methods). The momentum distribution of 6 Li is given by the Fermi-Dirac distribution fli FD (E Li ), with E Li = p 2 Li /2m Li. The one of 4 K is approximated by the Maxwell-Boltzmann distribution fk MB(E K), with E K = p 2 K /2m K. The latter distribution does not change its momentum dependence with position, thus, no integration over space is needed to obtain the spectral response S ( ) d 3 p Li d 3 p K f FD Li (E Li ) f MB K (E K ) F (k) δ( E m + E r + ), (6) where F (k) is the Franck Condon overlap of the initial wavefunction with the molecule wavefunction. In our case the interaction in the initial state is negligible and F (k), as given in Ref. 16, reduces to F (k) (E r /E 3 b )1/2 (1 + E r /E b ) 2. The parameter E b is the binding energy of a molecule in vacuum at a resonance with finite effective range and reads E b = h 2 /(2m r a 2 ) with the parameter 1 a = r e /( 1 2r e /a 1). In the calculation of F (k), we do not account for interactions with the Fermi sea. Because of this approximation, we apply the model only for 1/(κ F a) < 1. For fitting the model line shapes to the experimental data, adjustable parameters are the individual heights of the spectra and the center of the Feshbach resonance. The latter parameter is required to be the same for all data sets in Fig S2. Independently determined parameters are k B T /ε F =.16 and ε F = h 37 khz. The model (solid lines) reproduces our data remarkably well. It allows us to pinpoint the resonance position to B = (2)G. This determination of B relies on our theoretical model to calculate E m. To test this model dependence, we replace E m simply by the binding energy of the molecule in vacuum plus the mean field energy, considering the corresponding atom-dimer scattering length 17. Using this simple model, the fit yields a resonance position that is 1 mg higher, which shows that the model dependence causes only a small systematic uncertainty. Moreover, the statistical fit uncertainty and the field calibration uncertainty are about 1 mg each. For T = and all other parameters unchanged, the model provides the dashed lines in Fig S2. The spectra show a sharp drop at = E m (4/46)ε F, which corresponds to the association of an impurity at rest and a majority atom at the Fermi edge. In an equal-mass mixture this process would occur at = E m (1/2)ε F. Thus, the width of the MHC in the two-body approximation is much larger for a heavy impurity than it is for an equal-mass impurity and it is even narrower for a light impurity. The true zero temperature ground state is actually at the energy E m ε F, a molecule at rest formed from a 4 K atom at rest and a 6 Li atom at the Fermi edge. However, to reach this state, momentum conservation requires a higher-order process, i.e. the scattering of at least one additional 6 Li atom from and to the Fermi surface. Such processes are not included in the model presented here, which only considers the direct association of two atoms by an rf photon. In the strongly interacting regime the spectral function of the molecule shows additional excitations above the molecular ground state 13. This leads to an extension of the MHC spectral response above E m, of which we find clear indications in our data. The lower panel in Fig S2 shows finite signal above E m and the extension above E m is very evident in the strongly interacting 6

7 SUPPLEMENTARY INFORMATION RESEARCH regime, see Fig. 2b. 4 Decay rate of the repulsive polarons We analyze the decay of the repulsive polarons by assuming that they decay into well defined attractive polarons or well-defined molecules. In this quasiparticle picture, the decay is associated with the formation of a particle-hole pair in the Fermi sea to take up the released energy. In this sense, the decay into the attractive polaron is a 2-body process and the decay into the molecule is a 3-body process. We calculate the decay rate for these two channels by including them into the polaron self energy using a pole expansion of the 4 K propagator writing G(k,ω) Z + /( hω E + h 2 k 2 /(2m K )) + Z /( hω E h 2 k 2 /(2m K )) and a pole expansion of the T-matrix writing T (k,ω) Z m g 2 /( hω (E m ε F ) h 2 k 2 /(2M)). Here, Z ± is the quasiparticle residue of the repulsive and attractive polaron respectively and Z m the quasiparticle residue of the molecule. The factor g 2 = 2π h 4 /(m 2 ra 1 2r e /a) is the residue of the vacuum T-matrix for a general resonance. The details of this approach are given in Refs. 7, 18, the only difference being that here we include the effects of the finite effective range. The imaginary part of the self energy gives the decay rate of the wavefunction and we thus take twice the imaginary part to calculate the population decay. The 2-body decay into the attractive polaron and an additional particle-hole pair is calculated numerically to all orders in the T-matrix by inserting the pole expansion for the 4 K propagator in the self energy in the ladder approximation. For the 3-body decay into a molecule and an additional particle-hole pair, we include terms containing two 6 Li holes in the 4 K self energy 18, and an expansion to second order in the T-matrix relevant for 1/(κ F a) 1 yields ( ) Γ PM 64κ Fa Z+ 3 ( 45π m ) 5 Li 3/2 hκ F a ε mli M 2(E+ E m + ε F ) a 1 2r e /a F h. (7) m 2 K For simplicity, we have taken Z m = 1, which is an appropriate assumption for 1/(κ F a) 1. The effect of the narrow resonance on the decay rate enters through the quasiparticle residue Z +, the energies E +, E, E m and directly through the effective range r e. This decay rate has the same a 6 dependence as the three-body decay in vacuum in the limit of a broad resonance derived in Ref. 19. The numerical prefactor however differs since we have included the effects of the Fermi sea in a perturbative calculation. The results for the decay rates of repulsive polarons are shown in Fig. S3. The experimental data agree well with the theoretical results obtained for our narrow resonance (continuous lines) as already shown in Fig. 3 in the main text. For comparison, we also show the decay rates one would obtain in the limit of a broad resonance (dashed lines). We find that as magnitude of the effective range increases with respect to the interparticle spacing, the dominant two-body decay is strongly suppressed. This suppression is mainly due to a large reduction of the attractive polaron residue Z. Instead, the weaker three-body decay increases, which we attribute to the reduction of the polaronmolecule energy difference E + E m + ε F. Taking both decay rates together, the decay rate is at least an order of magnitude smaller at our narrow resonance as compared to the case of a broad resonance. It is important to note that this strong suppression of the decay at a given 1/(κ F a) cannot be simply attributed to the effective resonance shift at our narrow Feshbach resonance as 7

8 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 3: Decay rates of repulsive 4 K polarons in a Fermi sea of 6 Li atoms, shown as a function of interaction strength (left) and of the energy of the repulsive polaron (right). Blue and red lines represent the two- and three-body contributions, respectively, while data points are the experimental findings as also shown in Fig. 3 of the main text. The results for the moderately narrow resonance under study here (solid lines) is compared with the theoretical results obtained for the universal limit of a very broad resonance (dashed lines). The experimental values of E + are obtained by interpolation of the narrow peak position data peak, see Fig. S1d. discussed in Sec. 2. When taking this shift into account, a suppression factor of five to ten remains. To highlight this point, we choose a representation that is independent of the interaction parameter and that gives the dependence on the polaron energy, a direct manifestation of strong interactions. The right panel shows the same data and calculations as a function of E +. Also for a given E +, the repulsive polaron at our narrow resonance turns out to be much more stable than the repulsive polaron at a broad resonance. 5 Decay of repulsive polarons to molecules The decay of the repulsive polarons, shown in Fig. 3 of the main text, is measured by applying a special three-pulse scheme (see Methods). In this section we exploit the flexibility of this scheme to study the decay to lower-lying energy states in more detail. At a given interaction strength 1/(κ F a)=.9, we demonstrate that the repulsive polarons decay to molecules by showing that an rf spectrum taken after decay perfectly matches a reference spectrum of molecules. To populate the repulsive polaron branch, as done for the measurements of the decay rate, we tune the energy of the first pulse to E +, corresponding to =.16ε F at 1/(κ F a)=.9. The pulse duration (t p =.6ms) and the intensity are set to correspond to a π-pulse in the noninteracting system. The second pulse removes the remaining non-transferred atoms by transferring them to a third spin state. In contrast to the decay measurement presented in the main text, we here use much more rf power for the third pulse to be able to efficiently dissociate molecules. For this pur- 8

9 SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 4: Decay of repulsive polarons to molecules at 1/(κ F a)=.9. (a) The black squares (red dots) show the spectrum right after (2 ms after) the repulsive polaron has been populated. The blue diamonds show the dissociation spectrum of molecules for reference. The signal is the fraction of atoms transferred from the interacting spin state 1 to the noninteracting spin state. Note that the polaron peak at positive detuning is highly saturated and thus its signal is not proportional to the number of polarons. (b) The rf energy detuning is fixed to = 1.3ε F and the signal is recorded versus hold time. The error bars indicate the statistical uncertainties derived from at least three individual measurements. pose, we set t p =.3ms and the pulse area corresponds to a 3π-pulse in the noninteracting system. By varying the rf detuning, we record spectra for zero hold time (black squares) and for a hold time of 2ms (red dots), see Fig. S4a. The peak at small positive detuning shows the back-transfer of repulsive polarons. The corresponding signal decreases with hold time, signalling the decay of the repulsive polaron. In addition, a wide continuum in a range of negative detunings rises with increasing hold time. Such a wide continuum involves coupling to high momentum states, signaling a short distance between 4 K and 6 Li. To confirm that this continuum stems from molecules, we compare it to a reference spectrum of the dissociation of molecules (blue diamonds). We find a perfect match. To take such a reference spectrum, only the detuning of the first rf pulse is changed to directly associate molecules in the MHC instead of populating the repulsive polaron branch. We achieve a good association efficiency with =.54ε F and t p =.5ms. To study the evolution of the molecule population, which is fed by the decay of the repulsive polarons, we set the detuning of the third pulse to the peak of the molecule signal at = 1.3ε F and record the signal as a function of the hold time, see Fig. S4b. A simple exponential fit yields a rate of about 1 ms 1 =.43 ε F / h, which is in good agreement with the measured decay rate of the repulsive polaron at 1/(κ F a)=.9. The finite signal at zero hold time may have two origins. One contribution is some decay during the finite pulse durations of the three pulses, which are not included in the hold time. Another contribution may be the high momentum tail of the repulsive polarons as discussed in Ref. 15. Note that we do not find any second sharp peak at negative detuning, which would indicate 9

10 RESEARCH SUPPLEMENTARY INFORMATION Supplementary Figure 5: Linear increase of the Rabi frequency Ω with the unperturbed Rabi frequency Ω. The left (right) panel shows the driving to the repulsive (attractive) polaron. The solid lines are linear fits without offset and demonstrate the proportionality Ω Ω. the population of the attractive polaron branch. In case the repulsive polaron decays to the attractive polaron, the absence of the attractive polaron peak implies a very rapid subsequent decay of the attractive polaron to the MHC. Such a fast decay of the attractive polaron to the MHC is consistent with the very small signal of the attractive polaron peak throughout the regime of strong interaction as discussed in Sec. 2. Let us briefly discuss the possible role of inelastic two-body relaxation in the 6 Li - 4 K mixture, which is energetically possible as 4 K is not in the lowest spin state. This process was identified in Ref. 2 as a source of losses. However, this relaxation is about an order of magnitude slower than the measured decay rate of the repulsive polaron and thus does not affect our measurements. 6 Rabi oscillations and polaron quasiparticle residue For high rf power, the signal is well beyond linear response and the 4 K atoms exhibit coherent Rabi oscillations between the spin states and 1. In this regime the oscillations are so fast, that the polaron decay plays a minor role and can be ignored to a first approximation. The Rabi frequency depends on the matrix element of the rf probe between the initial state and the final state 1. Since the probe is homogenous in space, it does not change the spatial part of the atomic wavefunction and it can be described by the operator 21 ˆR Ω q (â 1qâq + h.c.) where â iq (â iq) creates (annihilates) a 4 K atom with momentum q in spin state i and Ω is the unperturbed Rabi frequency of the to 1 transition in the non-interacting case. Considering for simplicity an impurity at rest, the initial non-interacting state is given by I = â q= FS where FS is the 6 Li Fermi sea. The final polaronic state at zero momentum can be written as 1 F = Zâ 1q= FS + q< hκ F <p ϕ p,q â 1q pˆb p ˆb q FS +... (8) 1

11 SUPPLEMENTARY INFORMATION RESEARCH where ˆb q (ˆb q ) creates (annihilates) a 6 Li atom with momentum q. The second term contains a Fermi sea with at least one particle-hole excitation and thus is orthogonal to an unperturbed Fermi sea. Therefore the matrix element reduces to F ˆR I = Z Ω and we obtain the Rabi frequency Ω = Z Ω. (9) We neglect the momentum dependence of the quasiparticle residue and do not perform a thermal average over the initial states, which we expect to be a good approximation since T ε F /k B. In Fig. S5 we plot the observed Rabi frequency Ω as a function of the unperturbed Rabi frequency Ω. We find that the proportionality Ω Ω holds over a wide range of rf power. The measurements presented in the main text, taken at Ω = 2π 6.5kHz and 12.6 khz, are safely within this range. References 1. Chevy, F. Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations. Phys. Rev. A 74, (26). 2. Combescot, R., Recati, A., Lobo, C. & Chevy, F. Normal state of highly polarized Fermi gases: Simple many-body approaches. Phys. Rev. Lett. 98, 1842 (27). 3. Mora, C. & Chevy, F. Ground state of a tightly bound composite dimer immersed in a Fermi sea. Phys. Rev. A 8, 3367 (29). 4. Punk, M., Dumitrescu, P. T. & Zwerger, W. Polaron-to-molecule transition in a strongly imbalanced Fermi gas. Phys. Rev. A 8, 5365 (29). 5. Combescot, R., Giraud, S. & Leyronas, X. Analytical theory of the dressed bound state in highly polarized Fermi gases. Europhys. Lett. 88, 67 (29). 6. Prokof ev, N. & Svistunov, B. Fermi-polaron problem: Diagrammatic Monte Carlo method for divergent sign-alternating series. Phys. Rev. B 77, 248 (28). 7. Massignan, P. & Bruun, G. M. Repulsive polarons and itinerant ferromagnetism in strongly polarized Fermi gases. Eur. Phys. J D 65, (211). 8. Bruun, G. M., Jackson, A. D. & Kolomeitsev, E. E. Multichannel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects. Phys. Rev. A 71, (25). 9. Massignan, P. & Stoof, H. T. C. Efimov states near a Feshbach resonance. Phys. Rev. A 78, 371 (28). 1. Petrov, D. S. Three-boson problem near a narrow Feshbach resonance. Phys. Rev. Lett. 93, (24). 11

12 RESEARCH SUPPLEMENTARY INFORMATION 11. Massignan, P. Polarons and dressed molecules near narrow Feshbach resonances. Europhys. Lett. 98, 112 (212). 12. Ho, T.-L. & Cui, X. Alternative route to strong interaction: Narrow Feshbach resonance. arxiv: v2 (211). 13. Schmidt, R. & Enss, T. Excitation spectra and rf response near the polaron-to-molecule transition from the functional renormalization group. Phys. Rev. A 83, 6362 (211). 14. Ding, H. et al. Coherent quasiparticle weight and its connection to high-t c superconductivity from angle-resolved photoemission. Phys. Rev. Lett. 87, 2271 (21). 15. Schirotzek, A., Wu, C.-H., Sommer, A. & Zwierlein, M. W. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 12, 2342 (29). 16. Chin, C. & Julienne, P. S. Radio-frequency transitions on weakly bound ultracold molecules. Phys. Rev. A 71, (25). 17. Levinsen, J. & Petrov, D. S. Atom-dimer and dimer-dimer scattering in fermionic mixtures near a narrow Feshbach resonance. Eur. Phys. J. D 65, (211). 18. Bruun, G. M. & Massignan, P. Decay of polarons and molecules in a strongly polarized Fermi gas. Phys. Rev. Lett. 15, 243 (21). 19. Petrov, D. S. Three-body problem in Fermi gases with short-range interparticle interaction. Phys. Rev. A 67, 173 (23). 2. Naik, D. et al. Feshbach resonances in the 6 Li- 4 K Fermi-Fermi mixture: Elastic versus inelastic interactions. Eur. Phys. J. D 65, (211). 21. Massignan, P., Bruun, G. M. & Stoof, H. T. C. Twin peaks in rf spectra of Fermi gases at unitarity. Phys. Rev. A 77, 3161 (28). 12